Graph-guided Bayesian SVM with Adaptive Structured Shrinkage Prior for High-dimensional Data

Support vector machine (SVM) is a popular classification method for the analysis of a wide range of data including big biomedical data. Many SVM methods with feature selection have been developed under the frequentist regularization or Bayesian shrinkage frameworks. On the other hand, the value of incorporating a priori known biological knowledge, such as those from functional genomics and functional proteomics, into statistical analysis of -omic data has been recognized in recent years. Such biological information is often represented by graphs. We propose a novel method that assigns Laplace priors to the regression coefficients and incorporates the underlying graph information via a hyper-prior for the shrinkage parameters in the Laplace priors. This enables smoothing of shrinkage parameters for connected variables in the graph and conditional independence between shrinkage parameters for disconnected variables. Extensive simulations demonstrate that our proposed methods achieve the best performance compared to the other existing SVM methods in terms of prediction accuracy. The proposed method are also illustrated in analysis of genomic data from cancer studies, demonstrating its advantage in generating biologically meaningful results and identifying potentially important features.